Field of the Invention
The present invention concerns magnetic resonance imaging, and in particular a method and apparatus for magnetic resonance imaging wherein a signal model is used to generate a quantitative parameter map.
Description of the Prior Art
Magnetic resonance (MR) is a known modality with which images of the inside of an examination subject can be generated. Such a procedure is known as magnetic resonance imaging, or magnetic resonance tomography.
In simple terms, an examination subject is situated in a magnetic resonance apparatus in which a strong, static, homogenous basic magnetic field (also called a B0 field) is generated, having a field strength of 1.5 T Tesla, or more, which causes nuclear spins in the subject to become oriented along the direction of the basic magnetic field. Radio-frequency (RF) excitation pulses are radiated into the examination subject, which trigger the emission of nuclear magnetic resonance signals by the nuclear spins. These magnetic resonance signals are detected and are entered into a memory that is organized as k-space. The k-space data in the memory are used to reconstruct an image of the subject.
During the acquisition of the magnetic resonance signals, rapidly activated magnetic gradient fields are superimposed on the basic magnetic field, which spatially code the measurement data. These magnetic field gradients determine the points in the k-space memory at which the measurement data are entered. The acquired measurement data are digitized and stored as complex numerical values in k-space. An MR image can be reconstructed from k-space populated with such values by, for example, a multi-dimensional Fourier transform of the k-space data.
The contrast that is present in a magnetic resonance image is dependent on several physical properties of the nuclei that have been excited in order to obtain the MR data. The contrast that is present in an MR image is used to identify and characterize tissue properties that are shown in the image, ultimately for the purpose of diagnosing a pathological condition. Quantitative measurements in magnetic resonance imaging have recently gained much interest, such as calculation of the fat fraction (FF) and the transverse relaxation (R2*) from multi-gradient-echo images.
A typical way of determining quantitative parameters is to use a signal model, and to solve for the unknown model parameters, such as FF or R2*, given a series of measurements, e.g. multiple gradient-echo images.
It is typical that the signal model will contain constants that enter into the model. These constants can be associated with hardware of the magnetic resonance apparatus, such as receiver coil sensitivities, and those types of constants are typically measured in a calibration scan that takes place before the acquisition of the actual diagnostic MR data. The constants that enter into the signal model may also be given by the laws of physics, such as the Larmor frequency. Other constants that enter into the signal model are assumed to be known. An example of the latter category is the signal interference of water and triglycerides in the liver, which is typically determined once for each of a number of subjects, and then is assumed to be constant for all patients.
A general form of the signal model can be represented ass=function of (p,c,k)wherein s is the vector of acquired signals, p is the vector of unknowns, c is the vector of constants, and k is the vector of assumed constants.
An important quality measure of the fitting process is the residual, which is a well-known quantity in the field of statistics and optimization. In general terms, the residual of an observed value is the difference between the observed value and the estimated function value. This can be generally represented asr=s−s′=s−function of (p0,c,k)wherein p0 is the result of a fitting operation. From the residual and other variables, other, integral, measures for the quality of the fitting operation can be calculated, such as “chi squared,” or “r squared” or the “rms error.” These measures may be calculated inherently in the particular fitting algorithm used, and may constitute the “cost function” to be minimized.
Conventionally, the signal model constants in the third category are merely assumed to be known. As a consequence, any deviations from the true values of those constants lead to errors in the quantitative parameters to be determined. In some cases, the constants are reinterpreted as unknowns, and the relevant equation or equations are solved for these unknowns, along with the other unknowns. However, this is unfavorable since it makes the whole fitting operation less numerically stable, and the calculated quantitative parameters of interest more noisy.
An example of a signal model used in the context of chemical shift-based water/fat separation is described in the article “Chemical Shift-Based Water Fat Separation: A Comparison of Signal Models,” Hernando et al., Magnetic Resonance in Medicine, Vol. 64 (2010), pp. 811-822. The evaluation of the consistency of different signal models, by generating a quantitative parameter map, is described in “Signal Model Consistency Analysis of Different Protocols and Spectral Models in Multi Gradient Echo Liver PDFF and R2* Quantification,” Bacher et al., Proceedings of the International Society of Magnetic Resonance in Medicine, 22nd annual meeting (2014), p. 1672.
The parameters of the signal model correspond to, or correlate with, the measure or factor that is to be quantified. Examples are the apparent diffusion coefficient (ADC) as an exponential decay constant in a series of b-values, or transverse relaxation as another exponential decay constant in multi-echo acquisitions, or the fat/water signal modulation as interference constants in multi-echo acquisitions.
Additionally, there may be signal model parameters that describe confounding effects, such as inhomogeneity of the basic magnetic field (B0 inhomogeneity) in complex-valued signal fitting, or noise in magnitude-based signal fitting, or the temperature dependence of the water/fat spectrum. It has been proposed in the prior art that some of these parameters be used as variable parameters that are to be fitted as an additional degree of freedom, e.g. B0, or as precalibrated constants, e.g. noise or temperature.
In different signal model techniques, these additional parameters have either been included, or not included, in the signal model. Confounding factors or additional model parameters have been proposed for inclusion individually, and studies have been made to characterize the performance of these model variants, for example, their accuracy with respect to a reference standard. In quantitative fat/water/relaxation MR measurements, multi-step approaches are known as described, for example, in United States Patent Application Publication No. 2014/0128785, and the use of a spectral model of a multipoint Dixon technique is described in United States Patent Application Publication No. 2015/0061672. The disclosures of United States Patent Application Publication No. 2014/0126795 and United States Patent Application Publication No. 2015/0061672 are incorporated herein by reference.
U.S. Pat. No. 5,378,987 describes temperature measurements based on chemical shift, by analyzing a phase difference map.
Additionally, region of interest (ROI) analysis is known, but typically is used only manually and retrospectively, for parameter evaluation.